论文标题
超级流体涡流多物和圆环上的孤子条纹
Superfluid vortex multipoles and soliton stripes on a torus
论文作者
论文摘要
我们研究了圆环表面上非线性schrödinger（NLS）方程中涡旋偶极子和四极配置的存在，稳定性和动力学。为此，我们使用了最近得出的圆环[phys。 Rev. A 101，053606（2021）]降低点涡流模型，该模型与完整的NLS演化非常吻合。鉴定了水平，垂直和对角线固定的涡旋偶极子，并沿着圆环纵横比和溶液的化学潜力持续。确定了这些解决方案的稳定窗口。我们还研究了固定的涡旋四线构型。在消除了由不变和对称性引起的类似溶液之后，我们发现总共有16种不同的构型，从水平和垂直排列四极杆到矩形和菱形四倍，到梯形和不规则的四肢。在NLS和降低的模型水平上，对最不稳定且潜在的稳定四极溶液的稳定性进行了监测。发现两种四极配置在圆环纵横比的小窗口上是稳定的，对于相对较大的参数窗口而言，发现少数四倍体非常弱。最后，我们通过一系列具有稳态涡流配置的分叉级联反应简要研究了深色孤子条纹及其连接。
We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.
